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2 years ago

Find vertex of f(x)=x^2+6x+10

Mathematics

1 answer:

dem82 [27]2 years ago

5 0

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The length of the hypotenuse of the right triangle is 25 cm, the length of one of the legs is 10 cm. What is the length of the s

sergejj [24]

Answer:

$\large\boxed{AD=21\ and\ CD=2\sqrt{21}}$

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem for calculate the length of CA:

$CA^2+CB^2=AB^2$

We have

$CA=x,\ CB=10,\ AB=25$

Substitute:

$x^2+10^2=25^2$

$x^2+100=625$ subtract 100 from both sides

$x^2=525\to x=\sqrt{525}\\\\x=\sqrt{25\cdot21}\\\\x=\sqrt{25}\cdot\sqrt{21}\\\\x=5\sqrt{21}\ cm$

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

$\dfrac{AD}{AC}=\dfrac{AC}{AB}$

We have:

$AD=y,\ AC=5\sqrt{21},\ AB=25$

Substitute:

$\dfrac{y}{5\sqrt{21}}=\dfrac{5\sqrt{21}}{25}$

$\dfrac{y}{5\sqrt{21}}=\dfrac{\sqrt{21}}{5}$ cross multiply

$5y=5(\sqrt{21})^2$ divide both sides by 5

$y=21\ cm$

If you mean the length of segment CD, then use the proportion:

$\dfrac{CD}{AD}=\dfrac{CB}{CA}$

Substitute:

$\dfrac{CD}{21}=\dfrac{10}{5\sqrt{21}}\\\\\dfrac{CD}{21}=\dfrac{2}{\sqrt{21}}\qquad\text{cross multiply}\\\\CD\sqrt{21}=42\qquad\text{multiply both sides by}\ \sqrt{21}\\\\21CD=42\sqrt{21}\qquad\text{divide both sides by 21}\\\\CD=2\sqrt{21}\ cm$

3 0

3 years ago

What is the length of segment BE? A) 2 B) 4 C) 6 D) 8

alex41 [277]

Answer:

4........

plz follow me....

6 0

2 years ago

...........................

enyata [817]

Answer:

The value of r to be out in the given formula is r = 0.048.

Step-by-step explanation:

The rate is given as 4.8%.

Now to put the value of interest in the given formula,

We need the value of r.

r = $\frac{r \%}{100} = \frac{4.8}{100} = 0.048$

Hence, the value of r to be out in the given formula is r = 0.048.

3 0

3 years ago

Find the Surface Area of the triangular prism * PLEASE HELP! ILL GIVE YOU BRAINIEST!!

kirill [66]

Answer:

Step-by-step explanation:

=12 * 2 = 24

=3 * 2 = 6

=5 * 2 = 10

= 24 + 6 + 10 =40

8 0

3 years ago

Which represents the solution(s) of the system of equations, y = -x2 + 6x + 16 and y = - 4x + 37? Determine the solution set

AysviL [449]

Answer:

The answer is c

Step-by-step explanation:

(7,9) (3,25)

3 0

3 years ago